An expensive watch is powered by a 3-volt lithium battery expected to last three years. Suppose the life of the battery has a standard deviation of 0.3 year and is normally distributed.a. Determine the probability that the watch's battery will last longer than 3.8 years.b. Calculate the probability that the watch's battery will last more than 2.15 years.c. Compute the length-of-life value for which 15% of the watch's batteries last longer.
a. The probability that the battery will last longer than 3.8 years is
b. The probability that the battery will last more than 2.15 years is
c. The length-of-life value for which 15% of the batteries last longer is years.
In: Statistics and Probability
The truck traffic on a highway can be describe as a Poisson
process with a mean arrival rate of 1.5 trucks per minute. The
weight of each truck is random and the probability that a truck is
overloaded is 5%.
a. What is the probability that there will be at least
two trucks passing a weigh stat ion this highway in a 10-minute
period? Define the random variable.
b. What is the probability that at most one of the next
10 trucks stopping at the weigh station will be overloaded? Define
the random variable.
c. Suppose the weigh station will close for 30 minutes
for lunch. What is the probability of overloaded trucks passing the
weigh station during the lunch break? Define the random
variable.
In: Statistics and Probability
Finding Binomial Probabilities Mr. Taylor filled out a bracket for the NCAA National Tournament. Based on his knowledge of college basketball, he has a 0.45 probability of correctly picking the winner of a game in the tournament. The NCAA National Tournament has 32 first round games. Round each answer to 3 decimal places.
What is the probability Mr. Taylor will pick all 32 of the first round games correctly?
What is the probability Mr. Taylor will pick exactly 8 games correctly in the first round?
What is the probability Mr. Taylor will pick exactly 22 games incorrectly in the first round?
In: Statistics and Probability
1)Design the sample space for an experiment where you will flip three coins into the air, first one, then the second, and finally the third to examine the faces landing upwards. Use the sample space to answer the questions that follow. Probabilities should be expressed as decimals.
A) Please identify the sample space for this experiment.
B) What is the probability of at least one head showing?
C) What is the probability of exactly one tail showing?
D) What is the probability of all three coins matching?
E) What is the probability of a tail showing from the first flip, a head showing on the second flip? (either result on the third flip is included)
In: Statistics and Probability
4. Richard has just been given a ten-question multiple choice test in his history class. Each question has five answers only one of which is correct. Since Richard has not attended class recently, he does not know any of the answers. Assume that Richard guesses randomly on all ten questions.
(a) Find the probability that he will answer all ten questions correctly.
(b) Find the probability that he will answer five or more questions correctly.
(c) Find the probability that he will answer none of the questions correctly.
(d) Find the probability that he will answer at least three questions correctly.
In: Statistics and Probability
Precise Parts is a workshop that specializes in the production of electric motor shafts. For the E300 Electric Motor, the average axle size is the inches shown in the table below, with one standard deviation as shown in the same table. A normal distribution is considered to follow.
Average size Shaft (µ) 0.55in
Standard Deviation (σ) 0.10 in
What is the probability that a randomly selected axis is between
.55 and .65 inches?
• What is the probability that a randomly selected axis is greater than .65 inches?
• What is the probability that a randomly selected axis is between .53 and .59 inches?
• What is the probability that a randomly selected axis is less than .45 inches
In: Statistics and Probability
A family has four children, of age 3, 6, and 16 and 16 . Let’s assume that the probability of giving birth to a boy is the same as the probability of giving birth to a girl. Determine the following probabilities:
(a) that all 4 children are girls
(b) that at least two of the children are boys
(c) that the oldest child is a girl
(d) that only three children are of the same gender
(e) Given that you know that at least one child is a girl, what is the probability that the other three children are boys? TIP: This is a conditional probability question, where we are asking for P(BBB|G), where B and G stand for boy and girl, respectively.
In: Statistics and Probability
A box in a certain supply room contains five 40-W lightbulbs,
seven 60-W bulbs, and six 75-W bulbs. Suppose that three bulbs are
randomly selected. (Round your answers to four decimal
places.)
(a) What is the probability that exactly two of the selected bulbs
are rated 75-W?
(b) What is the probability that all three of the selected bulbs have the same rating?
(c) What is the probability that one bulb of each type is selected?
(d) Suppose now that bulbs are to be selected one by one until a
75-W bulb is found. What is the probability that it is necessary to
examine at least six bulbs?
In: Statistics and Probability
1. The time need to complete a final examination in a college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes.
In: Statistics and Probability
1. The time need to complete a final examination in a college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes.
In: Statistics and Probability